MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
23 
19. Let y, y', y t denote generally the orientations of the major axes of the molecular 
orbits of the incident, reflected and refracted rays, which, in the case of plane polar- 
ized rays, are the same as the angles which the planes of vibration make with the 
plane of incidence (see No. 11). First, for a plane polarized incident ray, in which 
case c=0, we have 
k k 1 k 
tan y=^, tan y'=p tany,=^- 
Substituting for h' k' h t k t their values, we find 
tan y'= — 
k cos (0 + 0,) 
h cos (0—0,) 
tan 
COS (0 + 0 ,) 
' 'cos (0 — 0;) 
k 2 sin (0 + 0 ; ) 
sin (0 4- 0 ; ) 
tan y=y ■ . “ v " =2 tan y . . 7 1 
' 1 h sin 20 + sin 20, ' sin 2 0 + sin 20, 
These formulae show the shiftings of the plane in which the vibrations are performed, 
and consequently of the plane perpendicular to this, which is usually called the plane 
of polarization. The first agrees with the formula, p. 361 of Airy’s Tracts, y, y'bein g 
of course the complements of the angles there denoted by u, (3, which formula is there 
stated to have been verified by numerous observations of Brewster and Arago. If 
the incident ray be elliptically polarized, the expressions for tan y, tan y', tan y, are of 
course more complicated. 
I have stated in No. 11, though for brevity the proof has been omitted, that in the 
2 hk /2 7tc\ 
tan 2y= ¥=F , cos 
hk /2w\ 
7f=j? cos (—)=(*’ 
2tany ^ 
1 — tan^y = 
tan 2 y+~ tan y— 1=0, 
tan y=— 2^±\/ 
general case, 
If we put 
we shall have 
whence 
and 
lo determine which sign ought to be used, we may observe that the expression ought 
k 
to reduce itself to ^ when c=0, as in the former case. But making c=0, we have 
P= 
hk 
tf-k*’ 
and the root becomes +^/ 
k h 
which reduces itself to j or — according as we take the upper or lower sign. The 
